Sorry if this is a stupid question, but I've seen hosts (including the host I'm with) offer zend optimizer. So exactly what is it?

Cheers,
Richie

http://zend.com/store/products/zend-optimizer.php

Zend Optimizer is a free application that runs the files encoded by the Zend Encoder while enhancing the running speed of PHP applications. It Increases runtime performance

It is Supported by PHP versions: 4.0.5 and above (4.0.4 in previous versions of the Zend Optimizer)
Supported operating systems: Linux glib 2.1 / 2.2 (e.g. RedHat 6.x/7.x, Debian 2.2, SuSE 6.4 / 7.2, Mandrake 8.1, and others), Sparc Solaris 2.x, FreeBSD 3.4 / 4.0, Windows(r) NT 4.0 / 2000 / XP.
Solaris i386, OpenBSD, & Mac OS X

It Increases runtime performance

Sometimes. It decreases it on other times (actually most times in my code base). Basically whether you get speed up or slowdown depends on the nature of your code There's actually quite a big hit for the optimisation process, so you only win if your code is of a certain structure that speeds up enough to overcome the hit. Badly written PHP may accelerate better than well designed code.

The only reliable way to get great acceleration is to use Zend Accelerator (non-free) or PHP Accelerator (free). Both deliver the same performance gains, typically 3 to 4 times, but up to 10 times gains have been benchmarked for some template based systems.